The dampers on a piano are the action parts which ‘dampen’ the sound of the strings when you lift your finger off the key of the piano. On an underdamper piano action the dampers are underneath the hammers therefore being slightly lower down the string than the dampers on an overdamper action. On an overdamper action the dampers are right at the top of the string above the hammers resulting in them not ‘damping’ the sound as efficiently as in the underdamper action. As with most things there are exceptions to this rule eg. Bluthner made a very good quality overdamper piano which had a far better damping mechanism than some inferior quality underdamper pianos.